Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.3 - More on Functions and Their Graphs - Exercise Set - Page 200: 122


See the explanation below.

Work Step by Step

To determine the type of function, substitute x by –x and compare it with f(x) as follows: If $f\left( -x \right)=f\left( x \right)$ , then the function is even. For example: $\begin{align} & \text{Let, }f\left( x \right)={{x}^{2}}+2 \\ & f\left( -x \right)={{\left( -x \right)}^{2}}+2 \\ & f\left( -x \right)={{x}^{2}}+2 \\ & f\left( x \right)=f\left( -x \right) \end{align}$ If $f\left( -x \right)=-f\left( x \right)$ , then the function is odd. $\begin{align} & \text{Let, }f\left( x \right)={{x}^{3}} \\ & \text{ }f\left( -x \right)={{\left( -x \right)}^{3}} \\ & f\left( -x \right)=-{{\left( x \right)}^{3}} \\ & f\left( x \right)=f\left( -x \right) \end{align}$ If $f\left( -x \right)\ne f\left( x \right)$ , then the function is neither even nor odd.
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